Fill in (2) in (1):
a=cca => c^2=1 => c=+1 or c=-1
Fill in (3) in (2)
b=aba => a^2=1 => a=+1 or a=-1
same for (1) in (2): b=+1 or b=-1
To satisfy all conditions at the same time, a, b and c all have to be +1 OR any two of them must be negative (e.g., a=b=-1, c=+1).
In all cases, abc=1